A383651 Expansion of 1/((1-x) * (1+4*x) * (1-6*x)).
1, 3, 31, 135, 1015, 5271, 34903, 196311, 1230295, 7172055, 43871191, 259871703, 1572651991, 9382224855, 56508097495, 338189591511, 2032573522903, 12181697242071, 73145159033815, 438651051877335, 2632785920566231, 15793197086188503, 94773256265966551
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (3,22,-24).
Programs
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PARI
a(n) = (6^(n+2)-2+(-4)^(n+2))/50;
Formula
a(n) = Sum_{k=0..n} 5^k * (-4)^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2).
a(n) = Sum_{k=0..n} (-5)^k * 6^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2).
a(n) = (6^(n+2) - 2 + (-4)^(n+2))/50 = (A083578(n+2) - 1)/25.
a(n) = 3*a(n-1) + 22*a(n-2) - 24*a(n-3).
E.g.f.: exp(-4*x)*(8 - exp(5*x) + 18*exp(10*x))/25. - Stefano Spezia, May 04 2025